This study focuses on steady axisymmetric flows of a Newtonian incompressible fluid through circular pipes with side inlets. Circular tubes with a set of holes along their sidewalls are used in a number of medical procedures as straight catheters to transfer fluid into or out of the human body. We argue that all previous work on the analogous problem of flow through porous ducts is inapplicable to the problem of fluid flow through side holes of a straight pipe, due to unrealistic side inlet conditions. In this paper, we present a linear, quasi one-dimensional analysis to predict the flux of fluid that each inlet transfers based on hydraulic resistivities of both the inlets and the duct. We also perform numerical simulations to predict this inlet flux for a more complicated three-dimensional case. Finally, we show that a nonlinear analysis is necessary to determine the resistivities for this complicated flow.

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